Question

Charge is placed on two conducting spheres that are very far apart and connected by a long thin wire. The radius of the smaller sphere is 5 cm and that of the larger sphere is 12 cm. The electric field at the surface of the larger sphere is 660 kV/m. Find the surface charge density on each sphere.

Answer 1

Answer:

surface charge density on each sphere is $440 \times 10^{-9}$ C

Explanation:

given data

radius of smaller sphere = 5 cm

radius of  larger sphere is 12 cm

electric field at surface of larger sphere = 660 kV/m = 660 × 1000 v/m

solution

we apply here electric field formula that is express as

E = $(\frac{1}{4\pi\epsilon })\times (\frac{Q_{1} }{R^{2} } )$    .................1

put here value

660000 = $9 \times 10^9 \times \frac{Q1}{0.12^2}$  

Q1 = 1056 × $10^{-9}$

and

here field inside a conductor is zero so that electric potential ( V ) is constant

$\frac{Q{1} }{R} = \frac{Q{2} }{r}$   ..................2

so Q2 will be

Q2 =  $\frac{5}{12} \times 1056 \times 10^{-9}$  

Q2 =  $440 \times 10^{-9}$  C